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A student must answer 7 out of 10 question on an examination

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A student must answer 7 out of 10 question on an examination

by swerve » Fri Mar 16, 2018 12:35 pm
A student must answer 7 out of 10 question on an examination. If at least 3 of the first 5 questions must be answered, how many possible combinations of 7 questions are available to the student?

A. 50
B. 80
C. 110
D. 220
E. 360

The OA is C.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
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by GMATinsight » Sat Mar 17, 2018 1:33 am
swerve wrote:A student must answer 7 out of 10 question on an examination. If at least 3 of the first 5 questions must be answered, how many possible combinations of 7 questions are available to the student?

A. 50
B. 80
C. 110
D. 220
E. 360

The OA is C.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
Case 1: 3 from first 5 and 4 from last 5 = 5C3*5C4 = 10*5 = 50
Case 2: 4 from first 5 and 3 from last 5 = 5C4*5C3 = 10*5 = 50
Case 3: 5 from first 5 and 2 from last 5 = 5C5*5C2 = 1*10 = 10

Total = 50+50+10 = 110

Answer: Option C
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